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The rank gradient from a combinatorial viewpoint

Miklos Abert·Andrei Jaikin-Zapirain·Nikolay Nikolov
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Abstract

This paper investigates the asymptotic behaviour of the minimal number of generators of finite index subgroups in residually finite groups. We analyze three natural classes of groups: amenable groups, groups possessing an infinite soluble normal subgroup and virtually free groups. As a tool for the amenable case we generalize Lackenby's trichotomy theorem on finitely presented groups.

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Miklos Abert, Andrei Jaikin-Zapirain, Nikolay Nikolov. 2011-02-15. The rank gradient from a combinatorial viewpoint. https://arxiv.org/abs/math/0701925

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